Chasing a modest 208 for 6 from their 50 overs, the South Africans tumbled to their third successive defeat when they were bundled out for 186 in 48.2 overs.
Warne, who finished with 4 for 40 from his 9.2 overs of leg spin, received fine support from the off spinner Tim May, who took 2 for 34 in his first match of the tournament.
Hansie Cronje, South Africa's vice-captain, top-scored with 64 and received the man of the match award, but his efforts were in vain as the rest of the team succumbed tamely.
Mark Taylor, Australia's captain, said: 'It was a great victory as we were defending a small total. If we keep winning in this way, I think we have a good chance of taking home the cup.' Praising Warne, Taylor remarked: 'The guy bowled really well and had the opposing batsmen in tangles.'
The South Africans, who desperately needed a victory to help them stay in the competition, had an early setback when Andrew Hudson was run out by smart fielding from Warne at mid-on after Kepler Wessels had refused a single.
Wessels was then joined by Cronje in the best partnership of 57 in 120 balls for the second wicket, May breaking the the stand when Wessels was taken at short fine leg top-edging an intended sweep. Jonty Rhodes followed next for 11, caught by David Boon as May induced another mistimed sweep, and when Cronje was fourth out at 124, the match slipped out of South Africa's grasp.
Warne, meanwhile, arrived to take out the tail by claiming the wickets of Eric Simons, Derek Crookes, Meyrick Pringle and Fanie de Villiers. He also owed a vote of thanks to the wicketkeeper Ian Healy, who made three smart stumpings.
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